If the cell is still live then normal cell functions can continue if it is supplied with food and oxygen, although it would be pointless to try to keep one cell alive when the rest of the body is dead. In the case of organ transplant, the brain dead body is kept alive on life support until the usable organs and tissues are harvested, then the remains are disposed of in whatever fashion has been dictated by the deceased or next of kin.

I had taken white blood cells and merged them with a bacteria and even without food and water the white blood cell/bacteria hybrids still functioned like normal white blood cells, they even had a immune response to foreign Viral Activity in the culture, so yes, even cells taken from a dead body that were still living would still function as they were in the body. This is a special case when being merged via biotechnology with a bacteria not requiring blood with oxygen but most cultures would require blood to oxygenate the cells to keep them alive. I made a thread about the White Blood cell/Bacteria Chimera cells being infected with chickenpox and still keeping their immune response to fight off the infection showing that even white blood cells that have been genetically altered still preform their job in the body which they started to clump up from all being freely floating in the culture. The battle that started months ago still continues to be fought to this day.